Information on Result #675165
Linear OA(3243, 19718, F3, 40) (dual of [19718, 19475, 41]-code), using construction X applied to Ce(39) ⊂ Ce(34) based on
- linear OA(3235, 19683, F3, 40) (dual of [19683, 19448, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(38, 35, F3, 4) (dual of [35, 27, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3244, 19719, F3, 40) (dual of [19719, 19475, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3242, 19717, F3, 39) (dual of [19717, 19475, 40]-code) | [i] | Truncation | |
| 3 | Linear OOA(3243, 9859, F3, 2, 40) (dual of [(9859, 2), 19475, 41]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3243, 6572, F3, 3, 40) (dual of [(6572, 3), 19473, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(3243, 4929, F3, 4, 40) (dual of [(4929, 4), 19473, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(3243, 3943, F3, 5, 40) (dual of [(3943, 5), 19472, 41]-NRT-code) | [i] | ||